One thing I'll point out is that I've heard quite a few people claim that Will Smith couldn't have been upset by the joke because he was laughing at it. First off, we only saw him chuckling a bit when the camera was pointed at him, and even then, there are multiple ways to read that.
Speaking from personal experience, I have a tendency to laugh when I'm in an uncomfortable situation to try to ease the tension for myself, not because I actually find the situation funny. I also tend to become very sarcastic in those situations, which tends to not help when the other person thinks I'm making fun of them or not taking them seriously because I'm "joking around".
I also wouldn't be surprised if Will Smith's laughter was the equivalent of those people who you know you've pissed off when they start smiling during an argument. Again, I'm one of those people. If you go back and watch Will Smith's reaction, don't just look at his chuckle, look at his body language and eyes. He does NOT seem actually amused to me.
Oh, and for the record, Will Smith has released an actual apology, it's just been overlooked by all the other discussion.